A366445 Triangle read by rows: T(n,k) = A023900(n/k)*phi(k) if k divides n, T(n,k) = 0 otherwise (n >= 1, 1 <= k <= n).
1, -1, 1, -2, 0, 2, -1, -1, 0, 2, -4, 0, 0, 0, 4, 2, -2, -2, 0, 0, 2, -6, 0, 0, 0, 0, 0, 6, -1, -1, 0, -2, 0, 0, 0, 4, -2, 0, -4, 0, 0, 0, 0, 0, 6, 4, -4, 0, 0, -4, 0, 0, 0, 0, 4, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 2, 2, -2, -4, 0, -2, 0, 0, 0, 0, 0, 4
Offset: 1
Examples
{
{1}, = 1
{-1, 1}, = 0
{-2, 0, 2}, = 0
{-1, -1, 0, 2}, = 0
{-4, 0, 0, 0, 4}, = 0
{2, -2, -2, 0, 0, 2}, = 0
{-6, 0, 0, 0, 0, 0, 6}, = 0
{-1, -1, 0, -2, 0, 0, 0, 4}, = 0
{-2, 0, -4, 0, 0, 0, 0, 0, 6}, = 0
{4, -4, 0, 0, -4, 0, 0, 0, 0, 4}, = 0
{-10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10}, = 0
{2, 2, -2, -4, 0, -2, 0, 0, 0, 0, 0, 4} = 0
}
Crossrefs
Programs
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Mathematica
nn = 12; g[n_] := DivisorSum[n, MoebiusMu[#] # &]; Flatten[Table[Table[If[Mod[n, k] == 0, g[n/k]*EulerPhi[k], 0], {k, 1, n}], {n, 1, nn}]]
Formula
T(n,k) = A023900(n/k)*phi(k) if k divides n, T(n,k) = 0 otherwise (n >= 1, 1 <= k <= n).
Comments